Castelli, Benedetto, Of the mensuration of running waters, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="068/01/053.jpg" pagenum="37"/>
            <p type="head">
              <s>PROPOSITION I.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The Sections of the ſame River diſcharge equal quan­
                <lb/>
              tities of Water in equal times, although the Secti­
                <lb/>
              ons themſelves he unequal.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let the two Sections be A and B, in the River C, running
                <lb/>
              from A, towards B; I ſay, that they diſcharge equal quan­
                <lb/>
              tity of Water in equal times; for if greater quantity of Wa­
                <lb/>
              ter ſhould paſs through A, than paſſeth through B, it would
                <lb/>
                <figure id="id.068.01.053.1.jpg" xlink:href="068/01/053/1.jpg" number="6"/>
                <lb/>
              follow that the Water in the intermediate ſpace of the River C,
                <lb/>
              would increaſe continually, which is manifeſtly falſe, but if
                <lb/>
              more Water ſhould iſſue through the Section B, than entreth at
                <lb/>
              the Section A, the Water in the intermediate ſpace C, would
                <lb/>
              grow continually leſs, and alwaies ebb, which is likewiſe falſe;
                <lb/>
              therefore the quantity of Water that paſſeth through the Secti­
                <lb/>
              on B, is equal to the quantity of Water which paſſeth through
                <lb/>
              the Section A, and therefore the Sections of the ſame River diſ­
                <lb/>
              charge,
                <emph type="italics"/>
              &c.
                <emph.end type="italics"/>
              Which w s to be demonſtrated.</s>
            </p>
            <p type="head">
              <s>PROPOSITION II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              In two Sections of Rivers, the quantity of the Water
                <lb/>
              which paſſeth by one Section, is to that which paſ­
                <lb/>
              ſeth by the ſecond, in a Proportion compounded of
                <lb/>
              the proportions of the firſt Section to the ſecond, and
                <lb/>
              of the velocitie through the first, to the velocitie
                <lb/>
              of the ſecond.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>I Et A, and B be two Sections of a River; I ſay, that the
                <lb/>
              quantity of Water which paſſeth through A, is to that which
                <lb/>
              paſſeth through B, in a proportion compounded of the pro­
                <lb/>
              portions of the firſt Section A, to the Section B; and of the velo­
                <lb/>
              city through A, to the velocity through B: Let a Section be </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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